Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral condensed phase

TL;DR

This paper analyzes the Landau-Peierls instability in a spatially modulated chiral phase, revealing that thermal fluctuations prevent true long-range order but allow algebraic correlations, akin to liquid crystal behavior.

Contribution

It demonstrates the Landau-Peierls instability in a Fulde-Ferrell type inhomogeneous chiral phase using a Landau-Ginzburg-Wilson framework, highlighting the anisotropic Nambu-Goldstone modes.

Findings

Long-range order is destroyed at finite temperature.

The phase exhibits algebraically decaying correlations.

The behavior is similar to liquid crystal phases.

Abstract

We investigate the stability of an inhomogeneous chiral condensed phase against low energy fluctuations about a spatially modulated order parameter. This phase corresponds to the so-called dual chiral density wave in the context of quark matter, where the chiral condensate is spatially modulated with a finite wavevector in a single direction. From the symmetry viewpoint, the phase realizes a locking of flavor and translational symmetries. Starting with a Landau-Ginzburg-Wilson effective Lagrangian, we find that the associated Nambu-Goldstone modes, whose dispersion relations are spatially anisotropic and soft in the direction normal to the wavevector of the modulation, wash out the long-range order at finite temperatures, but support algebraically decaying long-range correlations. This implies that the phase can exhibit a quasi-one-dimensional order as in liquid crystals.